Definition 3 Off-Policy Evaluation (OPE) [1]}:
Off-policy evaluation estimates the performance \(\mathbb {E}_{\pi _e}[G(\mathcal {H}_{T}^{\pi _e})|\mathcal {H}_T^{\pi _b}]\)  of \(\pi _e\)  based on a data set of trajectories \(\mathcal {H}_{T}^{\pi _b} \triangleq \lbrace S_0, A_1, Y_1, \cdots , S_t, A_t, Y_t, \cdots , S_{T-1}, A_T, Y_T \rbrace \)  each independently generated by different policy(ies) \(\pi _b\) .

